1 citations · 3 across the 17 of their papers we have counts for
18 papers
Graphs with many independent vertex cuts
Yanan Hu, Xingzhi Zhan, Leilei Zhang
The cycles are the only -connected graphs in which any two nonadjacent vertices form a vertex cut. We generalize this fact by proving that for every integer there exist…
The maximum degree of a minimally hamiltonian-connected graph
Xingzhi Zhan
We determine the possible maximum degrees of a minimally hamiltonian-connected graph with a given order. This answers a question posed by Modalleliyan and Omoomi in 2016. We also p…
On the metric subgraphs of a graph
Yanan Hu, Xingzhi Zhan
The three subgraphs of a connected graph induced by the center, annulus and periphery are called its metric subgraphs. The main results are as follows. (1) There exists a graph of…
Proof of a conjecture on hamiltonian-connected graphs
Petr Vrana, Xingzhi Zhan, Leilei Zhang
We prove that every 3-connected claw-free graph with domination number at most 3 is hamiltonian-connected. The result is sharp and it is inspired by a conjecture posed by Zheng, Br…
Regular homogeneously traceable nonhamiltonian graphs
Yanan Hu, Xingzhi Zhan
A graph is called homogeneously traceable if every vertex is an endpoint of a Hamilton path. In 1979 Chartrand, Gould and Kapoor proved that for every integer there exist…
On almost self-centered graphs and almost peripheral graphs
Yanan Hu, Xingzhi Zhan
An almost self-centered graph is a connected graph of order with exactly central vertices, and an almost peripheral graph is a connected graph of order with exactly $…